Overlap-weighted difference-in-differences: A simple way to overcome poor propensity score overlap

Limited propensity score overlap in difference-in-differences (DID) can severely undermine reliable estimation of the average treatment effect on the treated (ATT), especially when extreme propensity scores dominate. Building on “overlap weighting”, we introduce a new DID estimand that assigns higher weights to units with their propensity scores close to 0.5, while down-weighting units with extreme propensity scores. Under a conditional parallel trends assumption, the estimand becomes an overlap-weighted ATT. The corresponding DID estimator is obtained by a simple regression of the residualized outcome change on the residualized treatment group indicator. Simulations demonstrate that the estimator remains stable in settings with limited propensity score overlap, outperforming standard approaches in both bias and variance.